``Fuzzy CP²'', which is a four-dimensional fuzzy manifold analogous to the fuzzy 2-sphere (S²), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving the structure constant of the SU(3) Lie algebra. Although the fuzzy S², which is also a classical solution of the same model, has actually smaller free energy than the fuzzy CP², Monte Carlo simulation shows that the fuzzy CP² is stable even nonperturbatively due to the suppression of tunneling effects at large N as far as the coefficient of the cubic term (α) is sufficiently large. As α is decreased, both the fuzzy CP² and the fuzzy S² collapse to a solid ball and the system is essentially described by the pure Yang-Mills model (α = 0). The corresponding transitions are of first order. The gauge group generated dynamically above the critical point turns out to be of rank one for both CP² and S² cases. Above the critical point, we also perform perturbative calculations for various quantities to all orders, taking advantage of the one-loop saturation of the effective action in the large-N limit. By extrapolating our Monte Carlo results to N = ∞, we find excellent agreement with the all order results.